Question

Perot's business is booming. He believes he can now sell three times as many shirts and can get a 35% discount in purchase price by wielding his new power. He suggests ordering 3,000 shirts every other month. Do you agree with him? What numbers would you show him to support your answer. If he promises to pay you one-half of any savings you can create, how much money would you make?

Suppose you know that the annual backorder cost is $5.50 per shirt and that the data from the first part of the question apply. Would you suggest that Perot allow backorders? What would be your backorder level by the time you place your next order? Given the same promise by Perot, would you make any more money? If so, how much?

Original shirt cost $47.50

Annual holding cost is 22% of the purchase price of the shirt

Transaction cost is $25 each order

Answer 1

I do completely agree with Mr. Perot as his suggestion to order 3000 shirts every other month is quite economical.

Justification with calculations--------

At first we will compare it with application of EOQ technique

EOQ( Economic order quantity)=Sqrt( 2CO/I)

where C= Annual consumption = 18000 shirts(3000*6)

O= ordering cost per order=25$
I= Inventory carrying cost=10.45 (22% of unit cost = 47.50*22%=10.45)

EOQ= sqrt{ (2*18000*25)/10*45}
sqrt(900000/10.45)= sqrt86124.40

=293 shirts

*so,as per EOQ, he must order 293 shirts at one time

# let's compare it with current discount offer of 35% on purchase price on ordering 3000 shirts per order---------

COMPARATIVE TABLE(EOQ VS DISCOUNT OFFER)

Ordering quantity	number of orders	Annual total unit cost($)	Annual ordering cost($)@25	Annual carrying cost($) orderingqty/2*carryincostp/u	total annual cost ($)
293	18000/293=62	47*50*18000=855000	62*25=1550	293/2*10.45=1550(approx)	855000+1550+1550=858100
3000	18000/3000=6	30.875*18000=555750 (47.50-35% of 47.50=30.875)	6*25=150	3000/2*6.79=10185 (30.875*22%=6.79)	555750+150+10185=566085

As we evaluate the above two alternatives,we find that total cost of purchasing shirts is higher if we buy as per EOQ,as the total cost is much less with discount offer of 35%

$858100[ EOQ method]. > $555750[ discount offer]
so,I support Mr Perot .